Simplify the following expression: $x = \dfrac{r^2 - 2r - 3}{r - 3} $
First factor the polynomial in the numerator. $ r^2 - 2r - 3 = (r - 3)(r + 1) $ So we can rewrite the expression as: $x = \dfrac{(r - 3)(r + 1)}{r - 3} $ We can divide the numerator and denominator by $(r - 3)$ on condition that $r \neq 3$ Therefore $x = r + 1; r \neq 3$